A multiplicity result for quasilinear problems with convex and concave nonlinearities and nonlinear boundary conditions inunbounded domains

Electronic Journal of Differential Equations

关键词: Variational method;    fibering method;    Palais-Smale condition;    genus.;   

DOI  :  

来源: DOAJ

【 摘 要 】

We study the following quasilinear problem with nonlinear boundary conditions$$displaylines{ -Delta_{p}u=lambda a(x)|u|^{p-2}u+k(x)|u|^{q-2}u-h(x)|u|^{s-2}u, quad hbox{in }Omega,cr |abla u|^{p-2}abla ucdoteta+b(x)|u|^{p-2}u=0quad hbox{on }partialOmega, }$$where $Omega$ is an unbounded domain in $mathbb{R}^{N}$ with a noncompact and smooth boundary $partialOmega$, $eta$ denotes the unit outward normal vector on $partialOmega$, $Delta_{p}u=hbox{div,}(|abla u|^{p-2}abla u)$ is the $p$-Laplacian, $a$, $k$, $h$ and $b$ are nonnegative essentially bounded functions, $q$ less than $p$ less than $s$ and $p^{ast}

【 授权许可】

Unknown